Apparatus is known for depositing sheets on a stack, which apparatus is arranged downstream, for example, of a printing machine. Such apparatus uses grippers that are arranged on endless chains, open under cam control and allow a sheet to fall in order to form a stack. Allowing the sheet to fall can be improved by using suction air and blower devices, by the conveying speed being retarded considerably and by the falling movement being accelerated. In order to improve the exactness of the stack formation, the sheets to be deposited are brought up against a stop and aligned using rectilinear joggers acting on side edges. In the environment of the stack there is a large number of constructional elements requiring high outlay of materials and costs, which also impair operator accessibility to the stack for handling and inspection activities. The moving parts in the sheet stack area of a printing machine constitute a safety risk, so that the sheet stack area is enclosed to the greatest possible extent. In order to remove a proof sheet, appropriate additional apparatus, such as flaps or diverters, can be provided, which necessitates additional outlay.